OR
Cred weighting of Development and Expected Claim techniques,
The weight is based on % paid (or % reptd.), i.e. B-F Ult = % paid * Dev Ult + (1 - % paid) x Exp Clm. Ult
c. On a pattern that goes above 100% reported or paid, you’ll see this on lines with salvage + subrogation or short tailed lines with strong case reserves. The % reported amount (2) cannot go above 1 in credibility theory. Therefore, in this situation, in theory, the method shouldn’t be used.
OR
Would not apply if % paid is greater than 100% (violates credibility definition)
d. The reported method would be more responsive because the development method is responsive to increasing claim ratios, and the reported BF method will give more weight to the development method early on since % Rpt is often greater than % paid.
OR
Reptd is more responsive, since % reptd is usually greater than % paid, thereby putting more weight on the developed emerging exp. And less on the a priori estimate
S13 – Exam 5 - Question #18
e. Similarity: CC (Cape Cod) and BF methods both assume the unreported amount should be based off of another estimate and not developed as in the development technique. In other words, they both assume that experience to date in an AY doesn’t tell you everything about future development. Difference: The two methods calculated the “initial expected” ultimate differently. The BF method relies on an a priori selected loss ratio and the CC method calculates the LR (or PP) using the losses to date divided by the “used up” premium. Therefore the CC method is more responsive.
OR
Both methods are cred weighting of Dev &Exp Claims but B-F initial exp loss ratio is an a priori estimate, while Cape Cod determines IELR using reported losses & used-up premium
Examiner’s Report
a. The majority of candidates received full credit. Those that didn’t receive full credit typically lost points because they didn't differentiate between total claim versus unreported/unpaid claim.
b. The majority of candidates received full credit. Those that didn’t receive full credit were often mentioning the credibility calculation but were not mentioning to which method this factor would apply.
Another common mistake was to weight Z with [Actual loss / reported/ paid] instead of [Development Method Ultimate Loss/ reported / paid]
c. The majority of candidates did not receive full credit. A common mistake for candidates was that they were mentioning situation where BF method was not appropriate instead of referring to a situation where credibility weighting assumption itself of BF method was not appropriate.
d. The majority of candidates did not receive full credit. Most of the candidate identified the right method, but only a few had a clear explanation on why the reported method was more appropriate.
19. (3.25 points) Given the following information: Reported as of
Accident December 31, 2012 Payroll
Year Claim Counts Seventies ($000)
2010 1,549 $22,418 $63,438
2011 1,455 $18,730 $62,893
2012 1,023 $12,501 $67,005
Reporting Patterns
As of (Reported %)
Month Claim Count Seventies
12 85.0% 43.0%
24 95.0% 67.0%
36 98.0% 83.0%
The reported claim counts for accident year 2012 are unusually low due to a temporary slowdown of claims being opened.
Annual frequency trend = -2%.
Annual severity trend = +5%.
Annual payroll trend = +4%.
Use an appropriate frequency-severity technique to estimate the IBNR for accident year 2012 at December 31, 2012 and justify all selections.
S13 – Exam 5 - Question #19
AY 2012 ULT Losses = Sel PP x payroll ($100)
Sel PP = Trended and Developed Claim Counts * Trended and Developed Severity/Trended Exposures AY 2010 IBNR = AY 2012 ULT Losses – AY 2012 Reported Losses
= AY 2012 ULT Losses – AY 2012 (Reported Claim Counts * Reported Severities) Because 2012 frequency is off, severity is probably also impacted (smaller claims open faster), so 2012 will not be used in the calculation.
As of 12/31/2012, AY
Counts CDF Trend Trend + Dev counts (a)
2010 1,549 1/.98 .982 1518.02
2011 1,455 1/.95 .98 1500.95
Sev CDF Trend Trend + Dev sev (b)
2010 22,418 1/.83 1.052 29778.13
2011 18,730 1/.67 1.05 29352.99
Exposure Trend Trended Exp (c)
2010 63,438 1042 = 68,614.54
Trended PP
a
b
c
; 2010 = 658.81; 2011 = 673.57; Sel = Avg = 666.19 AY 2012 ULT Losses = Sel PP x payroll($100) = 666.19 x 67,005=44,638,060.95 AY 2010 IBNR = AY 2012 ULT Losses – AY 2012 Reported Losses= AY 2012 ULT Losses – AY 2012 (Reported Claim Counts * Reported Severities) = 44,638,060.95 – (1023) x 12501 = $31,849,537.95
OR
AY 2012 ULT Losses = Ultimate Trended Frequency * Ultimate and Trended Severity * payroll ($100) ULT and Trended Frequency = Trended Ultimate Counts/Trended Payroll
ULT Trended Severity = Reported Severity Cumulative Reported Severity % * Severity Trend AY 2010 IBNR = AY 2012 ULT Losses – AY 2012 Reported Losses
= AY 2012 ULT Losses – AY 2012 (Reported Claim Counts * Reported Severities)
Because 2012 frequency is off, severity is probably also impacted (smaller claims open faster), so
ULT claims Claim Trend Trended Ult Claims Trended Payroll = Payroll * Payroll Trend
1549/0.98 1.01922 = 1,642 63,438 x 1.042 = 68,615
1455/0.95 1.01921 = 1,561 62,893 x 1.041 = 65,409
1023/0.85 1.01920 = 1,204 67,005 x 1.040 = 67,005
Freq trend = Claim Trend / Payroll Trend = 0.98 = Claim Trend/1.04; Claim Trend = 1.0192
ULT and Trended Frequency = Trended Ultimate Counts / Trended Payroll 2010 Freq = 1,642/68,615= 0.0239
2011 Freq= 1,561/65,409 = 0.0239
→ Selected frequency trend = 0.0239
ULT Trended Severity = Reported Severity / Cumulative Reported Severity % * Severity Trend
22,418/0.83 x 1.052 = 29,778
18,730/0.67 x 1.05 = 29,353 12,501/0.43 x 1.00 = 29,072
→All Average Sel= 29,401
AY 2012 Ultimate = 0.0239 x $29,401 x $67,005 = $47,083,335 AY 2012 IBNR = $47,803,335 – 1,023 x $12,501 = $34,294,812
Selected Frequency based on 2010 + 2011 because 2012 had a slowdown in claim counts, making it project an inaccurately low ULT claim count.
Severity is still reliable because it is an average number i.e. average is based on counts and dollars. Used an all years average for stability.
S13 – Exam 5 - Question #19 OR
Ultimate Claims Trended Exposure Frequency 2010 1,549 /.98 = 1580 63,438 x 1.042 2.30%
2011 1,455 /.95 = 1532 62,893 x 1.04 2.34%
Trended Frequencies 2010 .023 (.98)2 = .0221
2011 .0234(.98) = .0229
Selected Frequency = Simple Average = .0225
Ultimate Severity Trended Ultimate Severity 2010
22, 418
27, 010
.83
29,779 201118, 730
27, 955
.47
29,353 201212, 501
29, 072
.43
29,072Selected Severity = Simple Average = .29,401
Ultimate Claims= 29,401 x .0225 x 67,005 = 44,325,315 IBNR= 44,325,315 - 1,023 x 12,501= 31, 536,792
Since AY 2012 claim counts were subject to a temporary slowdown they were removed from the calculation of the ultimate frequency because using the current report patterns would severely underestimate ultimate freq. for that year.
Severity was assumed to be unaffected since there was no mention of a change in claim department methodology, just a slowdown in opening all claims.
Examiner’s Report
Candidates generally performed well on the calculation portion of this question.
Some candidates did not calculate frequency (claim counts / payroll) and simply multiplied the average of 2010 and 2011 claim counts by a severity selection to determine 2012 ultimate claims. This does not account for the 2012 exposure levels and was not awarded full credit.
Some candidates calculated the ultimate loss indication correctly and subsequently lost points by failing to calculate the indicated IBNR associated with the ultimate loss. A small portion of candidates calculated the IBNR for all 3 accident years rather than just 2012.
Some candidates did not justify their selections, as specified in the question. Additionally, a portion of candidates simply wrote out their selection in words; for example, writing "select average of 2010 and 2011" does not constitute a justification and did not receive credit.
There were some candidates that spent time converting the percentage reported factors to loss development factors and subsequently multiplying by the claim counts and severities. The
mathematical equivalent of dividing by the percentage reported could have saved the candidates time. A smaller portion of candidates used the percentage reported figures to create triangles of counts and severities that were unnecessary and subsequently not used in their solution.
Common mistakes included:
Not using trend factors
Not using loss development factors
Applying loss development factors or trend factors to the incorrect year (for example, applying the 36-month factor to 2012 rather than 2010)
Assuming that the inverse of the given percentage reported factors were age-to-age factors rather than age-to-ultimate factors
20. (3 points) Given the following information for a line of business:
Assume no reported claims development past 36 months.
Annual claim severity trend = +5%.
Paid claim development method ultimate loss for accident year 2012 = $10,275,000.
Reported claim development method ultimate loss for accident year 2012 = $9,650,000,
Cumulative Paid Claims ($000s) Cumulative Closed Claim Count
Accident Accident
Year 12 Months 24 Months 36 Months Year 12 Months 24 Months 36 Months
2010 $2,100 $6,410 $8,300 2010 35 75 99
2011 $2,210 $7,000 2011 35 80
2012 $2,550 2012 40
Cumulative Reported Claims ($000s) Cumulative Reported Claim Count
Accident Accident
Year 12 Months 24 Months 36 Months Year 12 Months 24 Months 36 Months
2010 $5,300 $7,810 $8,500 2010 80 98 100
2011 $5,500 $8,130 2011 79 97
2012 $6,000 2012 82
Outstanding Claims ($000s) Outstanding Claim Count
Accident Accident
Year 12 Months 24 Months 36 Months Year 12 Months 24 Months 36 Months
2010 $3,200 $1,400 $200 2010 45 23 1
2011 $3,290 $1,130 2011 44 17
2012 $3,450 2012 42
Fully discuss the considerations in deciding between using the paid or the reported claim development method to estimate ultimate claims for this line of business, and recommend an ultimate loss estimate for accident year 2012.
S13 – Exam 5 - Question #20
Based on the given data, one should create triangles of various claim averages (i.e. avg. paid severities, avg. case o/s, avg. closed to reported counts, avg. reported severities) and analyze each for anomalies or trends in the data.
Check avg. paid severities:
AY 12 24 36 10 60 85.47 83.84 1.05 1.024 11 63.14 87.5 1.01 12 63.75 =7,000/80
Avg paid severities appears to be trending at rate less than 5% for most recent AY.
This could indicate a change in settlement practices; Insurer could be closing more small claims. Check Avg Case Outstanding: Avg Case out =
O/SClaim CountO/S $Claim
AY 12 24 36 10 71.00 60.87 200 1.05 1.09 11 74.77 66.47 1.02 12 76.19
Avg. case outstanding increased by less than 5% per year at 12 months and greater than 5% per year at 24 months. This could indicate a change in type of claim being closed at the pd.
Look at closed to reported ratios: Closed Ct/Rep Ct
AY 12 24 36
10 .4375 .7653 .99
11 .4430 .8247 =99/100
12 .4878
Closed to report count ratio appears to be increasingly, indicating a speed up in claim settlement. Since there is a speed up in settlement and avg. paid severity is trending at rate lower than 5%, it appears the insurer is closing more small claims quickly.
Look at avg rep clm
AY 12 24 36 10 66.25 79.69 85 1.05 1.05 11 69.62 83.81 1.05 12 73.17
Avg. Rep. CLM increasing at steady rate of 5%.
Examiner’s Report Question 20
Candidates were supposed to evaluate Average Paid (and/or Outstanding) and Average Reported trends and compare them to the known severity of 5%.
They should have noticed the increase in paid settlement and that reported trends matched the 5% severity.
From there they were to conclude to use the reported method and not the paid. This conclusion should have been reached by evaluating changes (or lack of change) in both case adequacy and settlement rates.
Many candidates calculated Average Paid and Average Case severities, but did not calculate the Average Reported severities. Most candidates did calculate trend from year to year.
Many of those lost credit by not making any statement on the stability or instability of the resulting trends.
Also, comparisons of the observed paid severity to the outstanding severity, or the observed severities along the diagonal rather than down the columns of the triangle did not receive full credit.
Many candidates that only looked at average paid and case and decided the change in trend of the case outstanding disproved using the reported method.
But case alone is inconclusive in determining reported stability.
Many of those candidates did not test for settlement rate changes, likely with the thought that they had identified the relevant piece of information to make their choice.
Some candidates further went on to test the settlement rate but did not see how an apparent case adequacy change is influenced by a real settlement rate change.
Those that did calculate Average Reported often noticed that the year to year trend was stable and some of those mentioned that the trend was consistent with the 5% severity.
A large number of candidates went off onto a Berquist-Sherman technique or an “adjusted” reported methodology which was incorrect as the reported method without adjustment is the preferred method.
Full credit for the selection of the reported method was given if the correct choice was made or even if the words “select the reported method” and no numerical choice was made.
If the candidate mistook the reported ultimate for incurred and then applied an LDF, or created their own LDF instead of using the ultimate given, full credit was still awarded.
If they adjusted the reported triangle using a BS or other methodology and then developed to ultimate, no credit was given for selecting the reported method.
The question asked the candidates to choose between the paid and reported methods.
Some candidates choose an average of them and got a number “Between.” Since the reported was accurate and the paid was not candidates did not receive full credit.
21. (2 points) Given the following information as of the December 31, 2011 actuarial valuation:
Accident Ultimate Reported Paid
Year Claims Claims Claims
2010 $1,200 $280 $125
2011 $1,300 $125 $75
Total $2,500 $405 $200
Cumulative Cumulative
Age in Percent Percent
Months Reported Paid
36 40% 12%
24 25% 10%
12 10% 5%
Given the following information as of December 31, 2012:
Accident Reported Paid
Year Claims Claims
2010 $470 $200
2011 $320 $175
Total $790 $375
a. (0.5 point) Based on the 2011 actuarial valuation, calculate expected paid claims for each accident year during calendar year 2012.
b. (0.5 point) Based on the 2011 actuarial valuation, calculate expected reported claims for each accident year during calendar year 2012.
c. (0.5 point) Discuss a scenario that explains any differences between actual and expected paid and reported claims as of December 31, 2012.
d. (0.5 point) Using the scenario discussed in part c. above, justify the selection of a reserving technique for estimating ultimate claims as of December 31, 2012.
S13 – Exam 5 - Question #21
Expected paid during CY 2012 = (Ult – Paid) / % Unpaid × (% Paid at 2012 - % Paid at 2011) a. Ultimate-Paid % unpaid developed in CY 2012
2010 1075 90%
1075 / .9
12% 10%
23.89
2011 1225 95%
1225
.1 .05
64.47
.95
ORExpected paid during CY 2012 = Ultimate Paid * x (% Paid at 2012 - % Paid at 2011) Yr Ult Paid % pd %pd age+12 % pd in age Exp paid in 2012
(1) (2) (3) (4)=(3)-(2) (1)*(4)
2010 1200 .10 .12 .02 24
2011 1300 .05 .10 .05 65
S13 – Exam 5 - Question #21 OR
Exp. Emergence ($) = Paid Claims x [Age to Age factor - 1.0]
Expected paid claims in CY 2012= Paid Claims x [Age to Ult x+12/ Age to Ult x – 1.0]
AY 2010 =
125
1
1
1
25
.10.12
AY 2011 =75
1
1
1
75
.05
.1
b.Expected reported during CY2012= (Ult – Rptd) / % Unrptd × (% Rptd at 2012 - % Rptd at 2011)
Ultimate-Reported % unreported 2010 920 .75
920 .4 .25 184 .75
2011 1175 .9
1175
.25 .1
195.83
.9
ORExpected reported during CY2012 = Ultimate Reported * x (% Paid at 2012 - % Paid at 2011)
Yr Ult Reported
% rptd %rptd age+12 % rptd in age Exp reported in 2012 (1) (2) (3) (4)=(3) – (2) (5)=(1)*(4) 2010 1200 .25 .4 .15 180 2011 1300 .1 .25 .15 195 375 OR
Exp. Emergence ($) = Reported Claims x [Age to Age factor - 1.0]
Expected reported claims in CY 2012= Reported Claims x [Age to Ult x+12/ Age to Ult x – 1.0]
AY 2010 =
280
1
1
168
.25.1
1
AY 2011 =125
1
1
1
187.5
.1.25
Question 21 (continued)
c. Using reported and paid claims as of 12/31/2011 and using the expected reported and expected paid from solution 1:
Reported at 12/31/2011 + Expected Reported Paid at 12/31/2011 + Expected Paid
2010: 280 + 184 = 464 125 + 23.89 = 148.89
2011: 125 +195.83 = 320.83 75 + 64.47 = 139.47
Actual Reported as of 12/31/2012 Actual Paid as of 12/31/2012
2010 = $470 2010 = $200
2011 = $320 2011 = $175
Expected reported is close to actual Expected paid is much less than actual The higher actual paid can be a result of speed up in the claim settlement.
OR
Increase in rate of claim settlement. The reported losses tracked quite close to expected, while the paid losses were much larger than expected.
OR
Reported claims expected are less than actual, so are paid claims. They could be understated due to change in the mix of business towards business with worse claim experience.
d. The actuary can use the reported development technique because the projected vs. actual
development was very close, and it is not affected by the speed up in claim settlement as the paid claim dev. method.
OR
I would use a reported dev. technique as it is not affected by decrease in settlement lag.
OR
I would suggest using the expected claims technique because you can judgmentally adjust the expected claims ration up due to the shift.
Examiner’ Report
a. Most candidates performed well , either applying the formula from the Friedland text or another reasonable estimation technique of expected loss emergence.
b. Most candidates performed well , either applying the formula from the Friedland text or another reasonable estimation technique of expected loss emergence.
c. Many candidates skipped this part. Some candidates focused on explaining the relatively minor difference in emerging reported losses while overlooking the more drastic difference in paid loss emergence. Other candidates described a scenario that would only partially explain the results derived in part a. and part b. Other candidates described scenarios that would result in the opposite results from those seen in part a. and part b., reversing the actual and expected losses. These responses generally received partial credit. d. Many candidates skipped part d. No credit was given for simply stating a reserve technique, as the question required the candidate to justify the technique. Some responses failed to link the response back to the scenario described in part c. as the question required.
22. (3 points) An actuary is assisting a manufacturing company in reserving its self-insured workers compensation program as of December 31, 2012. The program began on January 1, 1998 and has undergone the following changes in recent years:
On January 1, 2007, the per-occurrence retention was increased from $300,000 to $750,000.
On January 1, 2010, the company automated some of its production process. As a result, the company replaced a significant portion of its assembly-line staff with sales staff.
The actuary would like to use the following methods and data to estimate ultimate claims as of December 31, 2012:
Development method using company-specific claim development triangles.
Expected claims method using payroll as exposure base and the average of the reported and paid claim development projections as initial estimates of ultimate claims.
Frequency-severity method using company-specific claim count development triangles.
a. (1 point) Discuss necessary adjustments the actuary should make to the company-specific data to use the development method.
b. (1 point) Briefly describe four adjustments the actuary should consider making to historical claims and exposures to put them on current levels in the expected claims method. c. (1 point) Describe two diagnostic tests the actuary should perform before using the
frequency-severity method.
S13 – Exam 5 - Question #22
a. If possible, the actuary should restate the historical triangles to a $300k retention (one triangle) and to a $750K retention (a separate triangle) in order to remove the distortion that the change in retention would otherwise create. The actuary should then review these triangles separately and select LDFs to be applied to the appropriate retention by year.
OR
The actuary should adjust the claims data to be used in development method since the retention was increased from $300,000 to $750,000. The increase in retention will increase the claims reported and paid. Therefore, claims data before 2007 should be adjusted to current level before applying the development method. In addition, the change from assembly-line to sales will have an impact to the claims. Less injury will be expected when the company automated some of its production process. Hence, claims data before 2010 should be adjusted.
b. -Adjust the losses so they are on the 750,000 retention level by using ILFS.
-Adjust losses to account for the change in workers. Sales staff will have fewer losses (injuries) than assembly staff
-Adjust the exposures to account for inflation.
-Adjust the losses to account for benefit changes related to inflation. As the workers get raises, the losses will increase.
OR
1. Cap the historical claims, select large loss load 2. Apply loss trend
3. Apply benefit level change adjustment 4. Apply exposure trend
S13 – Exam 5 - Question #22
22c. (1 point) Describe two diagnostic tests the actuary should perform before using the frequency-severity method.
c. Look at the avg severity amount → claims/closed counts. The change in per occurrence retention could have an effect on severity.